Oriented Matroids
Oriented matroids appear throughout discrete geometry, with applications in algebra, topology, physics, and data analysis. This introduction to oriented matroids is intended for graduate students, scientists wanting to apply oriented matroids, and researchers in pure mathematics. The presentation is geometrically motivated and largely self-contained, and no knowledge of matroid theory is assumed. Beginning with geometric motivation grounded in linear algebra, the first chapters prove the major cryptomorphisms and the Topological Representation Theorem. From there the book uses basic topology to go directly from geometric intuition to rigorous discussion, avoiding the need for wider background knowledge. Topics include strong and weak maps, localizations and extensions, the Euclidean property and non-Euclidean properties, the Universality Theorem, convex polytopes, and triangulations. Themes that run throughout include the interplay between combinatorics, geometry, and topology, and the idea of oriented matroids as analogs to vector spaces over the real numbers and how this analogy plays out topologically.
2023-2024 Elementary School Contest Materials
This book contains one year of mathleague.org elementary school tests and answer keys: 7 qualifying-level test sets, one state-level test set, one national-level test set, and one international-level. Each test set contains a Sprint, Target, Team, and Number Sense test.
Introduction to Qualitative Methods for Differential Equations
Introduction to Qualitative Methods for Differential Equations provides an alternative approach to teaching and understanding differential equations.
A Mathematical Tour
A Mathematical Tour introduces readers to a selection of mathematical topics chosen for their centrality, importance, historical significance, and intrinsic appeal and beauty.
The Doctrine of Triangles
An interdisciplinary history of trigonometry from the mid-sixteenth century to the early twentieth The Doctrine of Triangles offers an interdisciplinary history of trigonometry that spans four centuries, starting in 1550 and concluding in the 1900s. Glen Van Brummelen tells the story of trigonometry as it evolved from an instrument for understanding the heavens to a practical tool, used in fields such as surveying and navigation. In Europe, China, and America, trigonometry aided and was itself transformed by concurrent mathematical revolutions, as well as the rise of science and technology. Following its uses in mid-sixteenth-century Europe as the "foot of the ladder to the stars" and the mathematical helpmate of astronomy, trigonometry became a ubiquitous tool for modeling various phenomena, including animal populations and sound waves. In the late sixteenth century, trigonometry increasingly entered the physical world through the practical disciplines, and its societal reach expanded with the invention of logarithms. Calculus shifted mathematical reasoning from geometric to algebraic patterns of thought, and trigonometry's participation in this new mathematical analysis grew, encouraging such innovations as complex numbers and non-Euclidean geometry. Meanwhile in China, trigonometry was evolving rapidly too, sometimes merging with indigenous forms of knowledge, and with Western discoveries. In the nineteenth century, trigonometry became even more integral to science and industry as a fundamental part of the science and engineering toolbox, and a staple subject in high school classrooms. A masterful combination of scholarly rigor and compelling narrative, The Doctrine of Triangles brings trigonometry's rich historical past full circle into the modern era.
A Mathematical Tour
A Mathematical Tour introduces readers to a selection of mathematical topics chosen for their centrality, importance, historical significance, and intrinsic appeal and beauty.
Engaging Young Student Math (V3)
Engaging Young Students in Mathematics through Competitions presents a wide range of topics relating to mathematics competitions and their meaning in the world of mathematical research, teaching and entertainment. Following the earlier two volumes, contributors explore a wide variety of fascinating problems of the type often presented at mathematics competitions. In this new third volume, many chapters are directly related to the challenges involved in organizing competitions under Covid-19, including many positive aspects resulting from the transition to online formats. There are also sections devoted to background information on connections between the mathematics of competitions and their organization, as well as the competitions' interplay with research, teaching and more.The various chapters are written by an international group of authors involved in problem development, many of whom were participants of the 9th Congress of the World Federation of National Mathematics Competitions in Bulgaria in 2022. Together, they provide a deep sense of the issues involved in creating such problems for competition mathematics and recreational mathematics.
Amusements in Mathematics
Unlock the Enigma of Numbers with a Timeless Classic! Dive into the captivating world of ""Amusements in Mathematics"" by the legendary Henry Ernest Dudeney, a masterpiece that has enchanted puzzle enthusiasts for generations. This extraordinary collection of mathematical puzzles and brainteasers, once out of print for decades, is now beautifully republished by Alpha Editions, making it a must-have collector's edition for both the curious minds of today and the inquisitive thinkers of tomorrow. From mind-bending riddles to ingenious conundrums, Dudeney's brilliance shines through every page, offering a delightful challenge to both novice and seasoned puzzle solvers. Whether you're looking to sharpen your problem-solving skills or simply seeking an entertaining escape into the world of numbers, this book promises hours of intellectual amusement. Don't miss your chance to own a piece of mathematical history that has stood the test of time. Rediscover the joy of puzzles with ""Amusements in Mathematics"" and let your imagination soar!
Lectures on Advanced Engineering Mathematics (With Worked Examples)
Course in Ordinary Differential Equations with Applications
This book was written for advanced undergraduate math or science majors. Its initial purpose was to illustrate the elementary mathematical theory of ordinary differential equations and their diverse and powerful applications. Historically these have been decisive in many physical problems, some of which have philosophically challenged and indeed altered our civilization's concepts. Because of the importance of the subject, the book is also suitable for a one-semester course for graduate students. The book consists of 12 chapters and six appendices.
Jewish Calendar Mathematics
This book begins with a short overview of calendars in general, and then delves deeply into Jewish calendar structure and mathematics. Details of how Torah portions are scheduled and how the structured triennial Torah reading and haftorah reading cycles work are explained. A comprehensive explanation of the calendrical aspects of Jewish holidays as well as the relationships between them and non-Jewish holidays is included. There are fourten appendices which allow even greater visibility into the material than does the main narrative by itself. This volume also includes substantial new material absent from the book's predecessor. A glossary is provided.
Differentiation of functions, Limited developments and Integration
Various Studies on Split and Non- Split Dominating Sets of an Interval
